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Weakly Non-Boussinesq Convection and Convective Overshooting in a Spherical Shell

AMS Seminar Series

Speaker: Lydia Korre, University of California, Santa Cruz

Presentation

Seminar Slide Deck (PDF-28.8MB)

Abstract

Motivated by stellar convection zones, we study Boussinesq convection in a weakly compressible gaseous spherical shell. We assume a constant adiabatic temperature gradient and employ more realistic boundary conditions for the temperature such that we have fixed flux at the inner boundary ri, which is what is set by the luminosity of the star, and fixed temperature at the outer boundary ro. We have run 3D numerical simulations using the PARODY code for three different model setups, which all assume that Pr= 0.1 (where Pr is the Prandtl number defined as the ratio of viscosity to thermal diffusivity) and a fixed aspect ratio ri/ro = 0.7. The simulation results all have the same notable properties for sufficiently large Ra (which is the Rayleigh number that is defined as the ratio of buoyancy to viscous forces) and considerably large variations in the superadiabaticity across the shell. In such simulations, we observe the remarkable emergence of a subadiabatic layer within the domain. However, convection remains vigorous everywhere across the shell, thereby indicating that it is a non-local process. Another important finding is that the mean kinetic energy E solely depends on the bulk Ra (for our fixed Pr and aspect ratio simulations) and not on other imposed parameters such as the superadiabaticity contrast. This is particularly useful for estimating E of a convective system and then using it in analytical models to evaluate other quantities, such as the convective flux.

We further extend our study to a two-layered system that consists of a convectively stable region below an unstable one. The layers are imposed via a chosen background temperature profile that transitions from superadiabatic to subadiatic. We study the dynamics of overshooting convection. The extension of the turbulent fluid motions from the CZ into the RZ depends on the stiffness of the RZ, the transition width between the two zones, and the Rayleigh number. We also find that the drop off in the mean kinetic energy below the CZ does not scale as an exponential as usually assumed in previous studies, but rather as a Gaussian whose width can be predicted a priori quite accurately from basic energetic arguments. These new findings will be particularly important in improving 1D stellar evolution codes.

Biography

Lydia Korre is a Ph.D. candidate in the Applied Mathematics and Statistics Department at the University of California, Santa Cruz (UCSC) working under the supervision of Prof. Nicholas Brummell and Prof. Pascale Garaud. She received her Diploma degree (Master equivalent) in Applied Mathematical and Physical Sciences from the National Technical University of Athens, and her MSc degree in Applied Mathematics and Statistics from UCSC. Her research is on fluid dynamics with particular applications to astrophysical problems.